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We theoretically find that finite size Fulde-Ferrell (FF) superconductor(which is characterized by spatially nonuniform ground state $\Psi \sim\text{exp}(-i{\bf q}_{FF}{\bf r})$ and $|\Psi|(r)=const$ in the bulk case,where $\Psi$ is a superconducting order parameter) has paramagnetic Meissner,vortex and 'onion' ground states with $|\Psi|(r) \neq const$. These states arerealized due to boundary effect when the lateral size of superconductor $L \sim1/q_{FF}$. We argue, that predicted states could be observed in thindisk/square made of superconductor-ferromagnet-normal metal trilayer with $L\simeq 150-600 nm$.

Paramagnetic Meissner, vortex and 'onion' ground states in Fulde-Ferrell finite-size superconductor